The present invention relates generally to apparatuses and methods for measuring a shape of a surface, and more particularly to an interferometer and an interference measurement method. The present invention is suitably used to measure a wide range of surface shapes from a spherical surface to an aspheric surface of a target object with high precision.
The present invention is also suitably used to measure surface shapes including a spherical surface, an aspheric surface, etc., of each optical element (e.g., a lens, a filter, etc.) in a projection optical system for use with a lithography process that transfers a pattern on a mask onto a photosensitive substrate, and manufactures a semiconductor device, etc.
Innovations in optical systems have always been provided by introductions of a new optical element and/or a degree of freedom. Among them, recent developments in process and measurement methods have successfully applied optical performance improved by the advent of aspheric surfaces, which has been sought in astronomical telescopes, to semiconductor exposure apparatuses used to manufacture semiconductor devices, which require extremely high accuracy.
There are three major advantages in a semiconductor exposure apparatus using an aspheric surface: The first advantage is the reduced number of optical elements. An optical system in a semiconductor exposure apparatus has necessarily required such expensive materials, as quartz and fluorite, as it requires a shorter wavelength. The reduced number of optical elements as an advantage of the aspheric surface is remarkably preferable for manufacture and cost-reduction purposes. The second advantage is miniaturization. The size reduction as another advantage of the aspheric surface still has drastically promoted manufacture and cost reduction. The third advantage is high performance. Aspheric surfaces are expected to play a more important role to realize an optical system that has increasingly required the high-accuracy performance as a high numerical aperture (“NA”) and low aberration advance.
A system using Extreme Ultra Violet (“EUV”) light is the likeliest to be elected for an exposure method of next generation to meet recent accelerating demands for the more minute patterns. The EUV system uses light having such a short wavelength as 13.4 nm, which is below one-tenth of a wavelength of light that has been used for conventional exposure, and a reflective image-forming optical system to transfer an image on a reticle onto a wafer. Wavelengths in the EUV range are too short for optical members (or transmissive materials) to transmit the EUV light, and the optical system uses only mirrors with no lenses. In addition, the EUV range restricts usable reflective materials, and mirror's reflectance for each surface is a little less than 70%. Therefore, such a structure as seen in conventional optical systems that use twenty or more lenses is not applicable in view of light use efficiency, and it is necessary to use optical elements as few as possible to form an image-forming optical system that meets desired performance.
Current EUV prototype machines use a three- or four-mirror system with an NA of about 0.10, but prospective systems are expected to use a six-mirror system with an NA of 0.25 to 0.30. As one solution for breaking down such a conventional wall and for realizing a high-performance optical system with fewer elements, it is the necessary technology to actually precisely process and measure aspheric surfaces so as to obtain an optical element with a predetermined surface shape.
However, even when a designed value provides high performance, a conventional aspheric-surface process disadvantageously has the limited measurement accuracy of the aspheric surface and cannot process a surface exceeding a predetermined aspheric surface amount, which is determined by a measurable range with desired precision. As is well known, the measurement and process are interrelated with each other; no precise process is available without good measurement accuracy.
The spherical-shape measurement technology is most commonly used technology to measure optical elements, and there are many general-purpose apparatuses with advanced precision due to continuous endeavors toward precision improvement. However, it is difficult for the aspheric surface amount ten times as large as a measuring wavelength to keep the same measurement precision as the spherical measurement since an interval in an interference fringe is excessively small.
Usually, the Computer Generated Hologram (“CGH”) or means for generating a wave front of a desired aspheric surface a dedicated null lens have been well known to measure large aspheric surfaces. However, these conventional approaches have been found to be unavailable for an optical system for semiconductor exposure apparatuses, regardless of whether they have other applications, because manufacture precisions for the CGH or null lens are insufficient for the semiconductor exposure apparatuses, and the CGH uses diffracted light and arduously requires 0-order light process.
There has been known another approach that measures aspheric surfaces using a mechanical or optical probe. Although the probe is so flexible that it is compatible with various shaped aspheric surfaces, the probe disadvantageously has measurement limits and its instable positional measurement. Therefore, this approach hardly provides so precise as an interference measurement method.
Moreover, a method of measuring an aspheric shape and an entire surface has been known which uses an interferometer for normal spherical shape measurements to measure only a segment (which has usually a strap shape) by gradually changing a radius of curvature to be measured. However, this problem includes the following disadvantages:
A target optical system is often co-axial, and thus its optical element often has a rotational symmetry. In general, an aspheric shape is described only by terms of even orders as in an equation (1) below where r is a distance from an optical axis (or a radius or a moving radius), c is a curvature of paraxial spherical surface, and z is the optical-axis direction:                     z        =                                            cr              2                                      1              +                                                1                  -                                                            (                                              1                        +                        K                                            )                                        ⁢                                          c                      2                                        ⁢                                          r                      2                                                                                                    +                      Ar            4                    +                      Br            6                    +                      Cr            8                    +                      Dr            10                                              (        1        )            
Where K=A=B=C=D=0 in the equation (1), z becomes a spherical surface with a radius of curvature R=1/c. Therefore, an offset amount (or aspheric surface amount) δ is defined as a subtraction of the spherical surface from the equation (1), which is expanded and expressed only by terms of fourth or higher orders of the distance r as in the following equation (2):                                                         δ              =                            ⁢                                                                    {                                                                                            1                          8                                                ⁢                                                  c                          3                                                ⁢                        K                                            +                      A                                        }                                    ⁢                                      r                    4                                                  +                                                      {                                                                                            1                          16                                                ⁢                                                  c                          5                                                ⁢                                                  K                          ⁡                                                      (                                                          2                              +                              K                                                        )                                                                                              +                      B                                        }                                    ⁢                                      r                    6                                                  +                                                                                                      ⁢                                                                    {                                                                                            5                          128                                                ⁢                                                  c                          7                                                ⁢                                                  K                          ⁡                                                      (                                                          3                              +                                                              3                                ⁢                                K                                                            +                                                              K                                2                                                                                      )                                                                                              +                      C                                        }                                    ⁢                                      r                    8                                                  +                                                                                                      ⁢                                                {                                                                                    7                        256                                            ⁢                                              c                        9                                            ⁢                                              K                        ⁡                                                  (                                                      4                            +                                                          6                              ⁢                              K                                                        +                                                          4                              ⁢                                                              K                                2                                                                                      +                                                          K                              3                                                                                )                                                                                      +                    D                                    }                                ⁢                                  r                  10                                                                                        (        2        )            
The term of the fourth order of the distance r is particularly important for an aspheric surface amount. When this offset amount δ exceeds ten times wavelength of measuring light, the measurement becomes difficult due to a too short interval between interference fringes.
As a solution for this problem, an outside of the initially measured area is measured by changing a radius of curvature of a reference aspheric surface to R′=1/c′. According to this method, the aspheric surface amount δ′ is expressed by the following equation (3):                                                                         δ                ′                            =                            ⁢                                                                    1                    2                                    ⁢                                      (                                          c                      -                                              c                        ′                                                              )                                    ⁢                                      r                    2                                                  +                                                      {                                                                                            1                          8                                                ⁢                                                                              c                            3                                                    ⁡                                                      (                                                          1                              +                              K                                                        )                                                                                              +                      A                      -                                                                        1                          8                                                ⁢                                                  c                          ′3                                                                                      }                                    ⁢                                      r                    4                                                  +                                                                                                      ⁢                                                                    {                                                                                            1                          16                                                ⁢                                                                                                            c                              5                                                        ⁡                                                          (                                                              1                                +                                K                                                            )                                                                                2                                                                    +                      B                      -                                                                        1                          16                                                ⁢                                                  c                          ′5                                                                                      }                                    ⁢                                      r                    6                                                  +                                                                                                      ⁢                                                                    {                                                                                            5                          128                                                ⁢                                                                                                            c                              7                                                        ⁡                                                          (                                                              1                                +                                K                                                            )                                                                                3                                                                    +                      C                      -                                                                        5                          128                                                ⁢                                                  c                          ′7                                                                                      }                                    ⁢                                      r                    8                                                  +                                                                                                      ⁢                                                {                                                            7                      256                                        +                                                                                            c                          9                                                ⁡                                                  (                                                      1                            +                            K                                                    )                                                                    4                                        +                    D                    -                                                                  7                        256                                            ⁢                                              c                        ′9                                                                              }                                ⁢                                  r                  10                                                                                        (        3        )            
As a coefficient c′ is properly selected, δ′<δ is available in this range. When the aspheric surface amount δ′ becomes more than about 10λ where λ is a measurement wavelength, the entire surface may be measured by varying the coefficient c′ and repeating measurements of the outside of the segment. However, as a speed of change at a peripheral of the surface is considered, terms of high orders of the distance r become important, such as sixth power and eighth power, whereby an interference-measurable segment becomes extremely narrow due to influence of these terms of high orders.
Therefore, a measurement of the entire surface would require a division into many segments and, in particular, the number of divisions increases at the peripheral of the surface, narrowing a width of a measurable segment. Since measured segments should be connected after each segment is measured, the sufficiently accurate measurement is not available due to erroneous superposition.